On c#-normal subgroups of finite groups
2016 ◽
Vol 16
(08)
◽
pp. 1750160
Keyword(s):
Let [Formula: see text] be a subgroup of a finite group [Formula: see text]. We say that [Formula: see text] is a [Formula: see text]-normal subgroup of [Formula: see text] if there exists a normal subgroup [Formula: see text] of [Formula: see text] such that [Formula: see text] and [Formula: see text] is a [Formula: see text]-subgroup of [Formula: see text]. In the present paper, we use [Formula: see text]-normality of subgroups to characterize the structure of finite groups, and establish some necessary and sufficient conditions for a finite group to be [Formula: see text]-supersolvable, [Formula: see text]-nilpotent and solvable. Our results extend and improve some recent ones.
1979 ◽
Vol 28
(3)
◽
pp. 335-345
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Keyword(s):
2010 ◽
Vol 09
(02)
◽
pp. 305-314
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1970 ◽
Vol 22
(1)
◽
pp. 41-46
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1962 ◽
Vol 5
(3)
◽
pp. 103-108
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1953 ◽
Vol 5
◽
pp. 477-497
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1969 ◽
Vol 21
◽
pp. 418-429
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Keyword(s):
Keyword(s):
2014 ◽
Vol 57
(3)
◽
pp. 648-657
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Keyword(s):